On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs

Akhlad Iqbal (), Shahid Ali () and I. Ahmad ()
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Akhlad Iqbal: Aligarh Muslim University
Shahid Ali: Aligarh Muslim University
I. Ahmad: Aligarh Muslim University

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 1, No 13, 239-251

Abstract: Abstract In this paper, we introduce a new class of sets and a new class of functions called geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold. The concept of E-quasiconvex functions on R n is extended to geodesic E-quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E-epigraph and discuss a characterization of geodesic E-convex functions in terms of its E-epigraph. Some properties of geodesic E-convex sets are also studied.

Keywords: Geodesic E-convex sets; Geodesic E-convex functions; Geodesic E-quasiconvex function; E-epigraphs; Riemannian manifolds (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-012-0052-3

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